User:ArekKulczycki - Revision history

ArekKulczycki: /* Proposition */

2024-09-30T19:43:19Z

‎Proposition

ArekKulczycki: /* Proposition */

2024-09-30T19:43:08Z

‎Proposition

ArekKulczycki: /* Offset */

2024-09-30T19:41:23Z

‎Offset

ArekKulczycki: /* Offset */

2024-09-30T19:40:13Z

‎Offset

ArekKulczycki at 19:38, 30 September 2024

2024-09-30T19:38:51Z

ArekKulczycki at 11:35, 30 September 2024

2024-09-30T11:35:28Z

ArekKulczycki at 11:32, 30 September 2024

2024-09-30T11:32:24Z

ArekKulczycki at 11:24, 30 September 2024

2024-09-30T11:24:18Z

ArekKulczycki at 11:23, 30 September 2024

2024-09-30T11:23:13Z

ArekKulczycki at 11:11, 30 September 2024

2024-09-30T11:11:11Z

@@ Line 79: / Line 79: @@
 A move annotated with ''Corner-Relative Coordinates'', if stone color is skipped, can occur twice in a game, because it means something else for each of the players. Inclusion of stone color is optional, but makes the notation objective. '''Moreover''', each move can be described in as much as in 4 ways, in a frame of reference of each of the corners. Naturally it only makes sense to use the closest one, but moves in center could be understood in multiple ways.
-Based on the reasoning above, we need to pack several values into each coordinate:
+Based on the earlier reasoning, we need to pack several values into each coordinate:
 * [Optionally] Color of the stone. It is optional, because usually we know what color the next move is. Nevertheless, to conform with various color standards let's use '''b''' for black and '''w''' for white, '''R''' for red and '''B''' for blue.

@@ Line 79: / Line 79: @@
 A move annotated with ''Corner-Relative Coordinates'', if stone color is skipped, can occur twice in a game, because it means something else for each of the players. Inclusion of stone color is optional, but makes the notation objective. '''Moreover''', each move can be described in as much as in 4 ways, in a frame of reference of each of the corners. Naturally it only makes sense to use the closest one, but moves in center could be understood in multiple ways.
-Based on what was said, we need to pack several values into each coordinate:
+Based on the reasoning above, we need to pack several values into each coordinate:
 * [Optionally] Color of the stone. It is optional, because usually we know what color the next move is. Nevertheless, to conform with various color standards let's use '''b''' for black and '''w''' for white, '''R''' for red and '''B''' for blue.

@@ Line 158: / Line 158: @@
     />
-Playing moves with an offset will determine the "shape" of your connection attempt. The shape that goes "around" the board I would call '''convex''', maybe popularly known as '''indirect'''. Instead a more '''direct''' shape that pushes through the middle I would call '''concave'''. Therefore convex moves (with positive offset) indicate an indirect strategy, while concave moves (negative offset) are an indicator of direct strategy. It sounds reasonable to propose these new terms when referring to the offset, the *convex/concave* moves for short.
+Playing moves with an offset will determine the "shape" of your connection attempt. The shape that goes "around" the board I would call '''convex''', maybe popularly known as '''indirect'''. Instead a more '''direct''' shape that pushes through the middle I would call '''concave'''. Therefore convex moves (with positive offset) indicate an indirect strategy, while concave moves (negative offset) are an indicator of direct strategy. It sounds reasonable to propose these new terms when referring to the offset, the '''convex/concave''' moves for short.
 == Joseki ==
 How to read joseki sequences? To be investigated...

@@ Line 151: / Line 151: @@
 == Offset ==
-The move offset has a practical strategical meaning for the game. A positive offset means the move is a "blocking" or "defensive" move next to the opponent side. A negative offset means the move is located around the middle of own edge, usually considered suboptimal, but strongly connected.
+The move offset has a strategical meaning for the game. A positive offset means the move is a "blocking" or "defensive" move next to the opponent side. A negative offset means the move is located around the middle of own edge, usually considered suboptimal, but strongly connected.
 <hexboard size="10x10"

@@ Line 138: / Line 138: @@
 '''And finally''' we calculate the offset, player-based:
-) take absolute coordinates, that is, <code>absolute_value:= board_size - prime_value</code>
+) for white player, from second coordinate (X) subtract the first (Y)
-) for white player, from second coordinate subtract the first (in absolutes)
+) for black player, from first coordinate (Y) subtract the second (X)
-−
-) for black player, from first coordinate subtract the second (in absolutes)
 '''Example:'''

@@ Line 25: / Line 25: @@
 '''a)''' replacing alphabet with numbers
-'''b)''' making measurements from the closest edges, instead of the further ones (with a caveat that it requires an additional flag to understand if it's a stone or it's mirror)
+'''b)''' making measurements from the closest edges, instead of the further ones (with a caveat that it requires an additional symbol to understand where the measurements is made from)
 ==== Challenge ====

@@ Line 40: / Line 40: @@
 ==== Exercise ====
-Alright, get ready, so black opens with <code>2'3</code>, white responds <code>45'</code> and they follow with <code>43'</code>, <code>33'</code>, <code>34'</code>, <code>53'</code>. You recognize it, right? No? Howcome, this is the most famous joseki! :)
+The realistic exercise is to just imagine a single move at a time, one by one:
-−
-Sorry, that was unfair, we are not trained at this as Hex players. The realistic exercise is to just imagine a single move at a time, one by one:
 * <code>6'3</code>
 * <code>75'</code>
 * <code>7'5</code>
-How long does it take you to figure out what move this is?
+How long does it take to figure out what move this is? Probably even more challenging is to read a sequence (11x11):
 == Reasoning ==
@@ Line 110: / Line 110: @@
 * <code>(7-2</code>
 * <code>)7-2</code>
 == Translations ==

@@ Line 33: / Line 33: @@
 I don't blame nobody, we didn't have anything else. But how many people use assymetrical coordinates like even 54, 45, let alone 37 or 96? The reason we don't do it is not that we forget which side to count from. The real reason is that the distance from edges in itself is not so meaningful in Hex after all!
-How about a test? Let's mark a move with a lone digit when counting from bottom/left and use [https://en.wikipedia.org/wiki/Prime_(symbol) Prime] notation if counting from top/right, similar to [https://www.hexwiki.net/index.php/User:Mason#Relative_Coordinates Mason Coordinates - the best system to my knowledge]. We use YX, that is, the column comes first and then the row. You're following so far?
+How about a test? Let's mark a move with a lone digit when counting from bottom/left and use [https://en.wikipedia.org/wiki/Prime_(symbol) Prime] notation if counting from top/right, similar to [https://www.hexwiki.net/index.php/User:Mason#Relative_Coordinates Mason Coordinates]. We use YX, that is, the column comes first and then the row. You're following so far?
 Let's talk about a game played on 13x13 board, so <code>11</code> is a bottom-left corner, <code>1'1'</code> is the top-right corner, got it? <code>1'1</code> is the top-left and <code>11'</code> is the bottom-right. Still with me?

@@ Line 62: / Line 62: @@
 '''Problem 2)''' The alphabet or a pair of numbers confusion.
-Let's use numbers only and forget about symmetry. We want to primarily reflect the distance from the corner. We can use a secondary number to distinguish between all the moves within the same distance from the corner.
+Let's use numbers only, but a primary and secondary number, such that their order has no ambiguity. We want to primarily reflect the distance from the corner. We can use a secondary number to distinguish between all the moves within the same distance from the corner.
 '''Problem 3)''' Practical intuition on where the move is located.
 As stated before, our reference points to understand the moves are corners. Specifically, we're interested if a move fits into the obtuse corner by a ladder and if it fits to the acute corner by a bridge.
-If it isn't a perfect fit, then we would be interested "how far off" it is. The moves can be "off" in two directions, may miss the target (our edge) or may fall into the edge too centrish. I will elaborate on this in an [https://www.hexwiki.net/index.php?title=User:ArekKulczycki#Offset Offset paragraph].
+If it isn't a perfect fit, then we would be interested "how far off" it is. The moves can be "off" in two directions: may "miss the target" (not be connected by a ladder/bridge) or may "fall into" the edge too centrish by a ladder/bridge. This feature I define as '''offset''' and elaborate on this in the [https://www.hexwiki.net/index.php?title=User:ArekKulczycki#Offset Offset paragraph].
 '''Problem 3')''' Relation between 2 moves.
-This might be the weakness of the corner-related approach, although with a smart interpretation (which I will do my best to provide) it's possible to also get a correct intuition.
 == Proposition ==
@@ Line 154: / Line 157: @@
 Playing moves with an offset will determine the "shape" of your connection attempt. The shape that goes "around" the board I would call '''convex''', maybe popularly known as '''indirect'''. Instead a more '''direct''' shape that pushes through the middle I would call '''concave'''. Therefore convex moves (with positive offset) indicate an indirect strategy, while concave moves (negative offset) are an indicator of direct strategy. It sounds reasonable to propose these new terms when referring to the offset, the *convex/concave* moves for short.

@@ Line 13: / Line 13: @@
 There have been attempts to create coordinate systems which are based on position of the stone in relation to both edges, which is logical and perfectly understandable approach. Obviously this is the way used in other board games and ourselves we annotate the boards this way, using letters for X coordinate and numbers for Y coordinate. This raises a question however... If we already have this notation, why do we still create new coordinate systems? Well, for a couple of reasons:
-'''1)''' We play on multiple board sizes, so a coordinate means a different thing on one or another board.
+'''Problem 1)''' We play on multiple board sizes, so a coordinate means a different thing on one or another board.
-'''2)''' The alphabet is confusing, as we don't know which in sequence is a letter, say, "k". However, having a pair of two numbers is confusing too, because if the coordinates are symmetrical then it's easy to confuse the order.
+'''Problem 2)''' The alphabet is confusing, as we don't know which in sequence is a letter, say, "k". However, having a pair of two numbers is confusing too, because if the coordinates are symmetrical then it's easy to confuse the order.
-'''3)''' The boards are really big... on a popular 19x19 board, it's hard to have even a slightest intuition what move we're describing when using YX coordinates.
+'''Problem 3)''' The boards are really big... on a popular 19x19 board, it's hard to have even a slightest intuition what move we're describing when using YX coordinates.
-'''3')''' On top of the objective intuition, it would be useful having 2 moves annotated, to easily see if they are adjacent or in a bridge relation.
+'''Problem 3')''' On top of the objective intuition, it would be useful having 2 moves annotated, to easily see if they are adjacent or in a bridge relation.
 So, back to my point, there have been attempts and they are still based on distances from edges. The values they introduce are the following:
@@ Line 56: / Line 56: @@
 If this is how I "find" my moves, why not base the coordinates off the same idea? That seems sensible, when I read a coordinate I will just mentally do what I always do: count steps from the corner and stop at the given distance. Let's see if this approach can solve the problems listed in the earlier paragraph.
-'''1)''' Independence on the board size.
+'''Problem 1)''' Independence on the board size.
 We're focused solely on corners/diagonals, so we're good to go, every board has the same 4 corners.
-'''2)''' The alphabet or a pair of numbers confusion.
+'''Problem 2)''' The alphabet or a pair of numbers confusion.
 Let's use numbers only and forget about symmetry. We want to primarily reflect the distance from the corner. We can use a secondary number to distinguish between all the moves within the same distance from the corner.
-'''3)''' Practical intuition on where the move is located.
+'''Problem 3)''' Practical intuition on where the move is located.
 As stated before, our reference points to understand the moves are corners. Specifically, we're interested if a move fits into the obtuse corner by a ladder and if it fits to the acute corner by a bridge.
 If it isn't a perfect fit, then we would be interested "how far off" it is. The moves can be "off" in two directions, may miss the target (our edge) or may fall into the edge too centrish. I will elaborate on this in an [https://www.hexwiki.net/index.php?title=User:ArekKulczycki#Offset Offset paragraph].
-'''3')''' Relation between 2 moves.
+'''Problem 3')''' Relation between 2 moves.
 This might be the weakness of the corner-related approach, although with a smart interpretation (which I will do my best to provide) it's possible to also get a correct intuition.